I created an arc when replacing a light bulb. Since then, the exhaust fan runs continuously. I have to use the breaker at the panel to shut off the fan. I suspect that I fried the control panel. Any thoughts?

You probably burned up some traces and welded a relay. You could try repairing the traces and replacing the relay. I've had very little success repairing these. Fixyourboard.com or corecentricsolutions.com can probably rebuild it and save you some money.

With the door closed, will the fan stop if you push up on the door handle to shift the door upwards?

On the handle end of the door, there are two tabs that engage switches that can affect operation. I had to take the control panel off and push the upper switch back into its socket and that fixed my JVM1653. Now it stays off when it should.